Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

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You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using std::max;
using std::min;
template <class T>
inline void read(T &x) {
  x = 0;
  int ne = 0;
  char c;
  while (!isdigit(c = getchar())) ne = c == '-';
  x = c - 48;
  while (isdigit(c = getchar())) x = x * 10 + c - 48;
  x = ne ? -x : x;
  return;
}
const int maxn = 200005;
const double eps = 1e-11;
const int inf = 0x7fffffff;
struct Seg {
  double l, r;
} seg[maxn];
double sum[maxn];
double sy, a, b;
int n, q;
int main() {
  scanf("%lf %lf %lf\n", &sy, &a, &b);
  sy = -sy;
  read(n);
  sum[0] = 0;
  for (register int i = 1; i <= n; i++) {
    read(seg[i].l), read(seg[i].r);
    sum[i] = sum[i - 1] + (seg[i].r - seg[i].l);
  }
  sum[n + 1] = sum[n];
  seg[0].l = seg[0].r = -1926081793.0;
  seg[n + 1].l = seg[n + 1].r = 1926081793.0;
  read(q);
  double x, y, xx, yy;
  int L = 0, R = n + 1;
  int px, py;
  double ans;
  while (q--) {
    read(x), read(y);
    xx = x - (x - a) * y / (y + sy), yy = x + (b - x) * y / (y + sy);
    L = 0, R = n + 1, px = 0;
    if (yy < seg[0].l || xx > seg[n].r) {
      puts("0.0000000000");
      continue;
    }
    if (eps < seg[0].l - xx)
      px = 0;
    else
      while (L <= R) {
        int mid = (L + R) >> 1;
        if (eps < xx - seg[mid].l)
          L = mid + 1, px = mid;
        else
          R = mid - 1;
      }
    L = 0, R = n + 1, py = n + 1;
    if (yy - seg[n].r > eps)
      py = n + 1;
    else
      while (L <= R) {
        int mid = (L + R) >> 1;
        if (seg[mid].r - yy > eps)
          R = mid - 1, py = mid;
        else
          L = mid + 1;
      }
    ans = sum[py - 1] - sum[px] + max(1.0 * 0, seg[px].r - xx) +
          max(1.0 * 0, yy - seg[py].l);
    ans = ans * (y + sy) / y;
    printf("%.7lf\n", ans);
  }
  return 0;
}